1. ECE 5221 Personal Communication Systems
Prepared by:
Dr. Ivica Kostanic
Lecture 3: Planning for Coverage in Cellular Systems
(Chapter 2.3 )
Spring 2011

2. Outline Mobile propagation environment
Free space path loss model (review)
Two ray propagation model (review)
Log distance path loss model (review)
Examples
Important note: Slides present summary of the results. Detailed derivations are given in notes.

3. Free space path loss model
Assumes free space between TX and RX
Realistic in microwave links to cellular towers
Not realistic in terrestrial propagation
Definition of quantities:
PT = power delivered to antenna terminals
GT = gain of transmit antenna
ERP = effective radiated power
FSPL = free space path loss
GR = gain of the receive antenna
PR = received power delivered to receiver
If the quantities are expressed in log-units:
Free space propagation scenario

4. Free Space Path Loss (FSPL)
Equation for FSPL (linear)
d = distance between TX and RX
l = wavelength of the RF wave
Equation for FSPL (logarithmic) – Frii’s equations
Notes:
FSPL grow 20dB/dec as a function of distance
FSPL grows 20dB/dec as a function of frequency
FSPL curves are straight lines in log-log coordinate system
Detailed derivation of Frii’s equations given in notes
FSPL curves 1-3GHz range

5. FSPL example:
Consider microwave communication link. Assume: power delivered to the antenna is 2W, transmit antenna gain is 20dB, the receive antenna gain is 5dB and minimum required signal level is -80dB. Estimate the maximum TX-RX separation for three frequencies: 1900MHz, 2.5GHz and 6GHz.
Answers:
For 1900MHz, distance 61.8 miles
For 2.5GHz, distance miles
For 6.6GHz, distance 1.58 miles
Notes:
Answers do not have any margin
RSL is received power expressed in dBm
Note decrease of distance with increase of frequency

6. Propagation in terrestrial environment
Three components of path loss
Separation between TX and RX
Log normal shadowing
Small scale fading
Exponential decay of signal level
Decay is expressed in X dB/dec
X is between 20 and 60
Additional path loss due to mobile being in a shadow of terrestrial objects
Modeled as a random variable normally distributed in log domain
Large variations of signal level over distances comparable to wavelength
Notes:
- First two components of the path loss predicted through macroscopic propagation models
- Third component is virtually unpredictable

7. Losses due to TX-RX separation
Simplified example: two-ray path loss model
Model derived for:
Flat Earth
Perfectly reflecting Earth
Assuming two ray addition at the RX point
Model predicts:
40 dB/dec loss as a function of distance
20 dB/dec dependence of losses on TX and RX heights
In practical situations:
Separation loss 20-60dB/dec (typical is still around 40dB/dec)
Dependence on antenna height still holds but is somewhat smaller (10-15 dB/dec)
Notes:
Detailed derivations are presented in notes

8. Example
Brevard County, FL has an area of 1,557 sq mi. Assume that the county is to be covered with a cellular system. The parameters of the cell sites are: Height of the tower: 50m, height of the mobile: 1.5m, maximum path loss 120dB. Use two-ray path loss model to determine:
Size of a cell
The number of circular cells required (neglect the overlap between the calls)
Cell count assuming that there is about 20% overlap between cells
Answers:
Radius of a cell is about 5.4 miles
The number of required cells is about 17
Taking the overlap into account, the number of required cells is 22

9. Typical RSL measurements
Log normal fading
Log normal shadowing introduces random variations of path loss
Random variations are modeled as a normal variable in log domain
Due to these variations the shape of cell is not regular
Practical problem:
Cover the area with irregularly shaped cells
Prevent excessive overlap between cells
Practical approach: Assume log distance path loss model
The form of the log distance model
Typical RSL measurements
RSL distance plot
Notes:
The model is straight line approximation
Variability captured by random variable

10. Log distance path loss model - details
Equation of the model
d0 – reference distance
PL – path loss in dB
PL0 – path in dB loss to reference distance
d – distance
m – slope
Xs – log normal fading in dB
Environment
Slope (dB/dec)
Free space 20
Terrestrial
20-50
Forested areas
Up to 60
In building
16-20
Microcell
16-25
Slope recorded in different us cities (after W.C.Y. Lee)

11. Standard deviation (dB)
Properties of fading
Probability density function
Standard deviation fading as a function of environment
Environment
Standard deviation (dB)
Rural
5-7
Suburban
6-8
Urban
8-10
Dense urban
10-12
Note: for nominal calculations standard deviation of 8dB is commonly assumed

12. Log distance path los model: example
Consider a cell site with ERP = 50dBm. Assume that the path loss follows log-distance path loss model. The following data are known: reference distance is 1 mile, reference path loss is 109dB, slope 38.4dB/dec. Calculate:
Median RSL at the distance of 3 miles
Probability that the signal is above level given in 1.
The RSL predicted by log-distance path loss model is -80dBm. Assume log normal shadowing with standard deviation of 7dB. Calculate probabilities:
RSL > -80dBm
RSL < -80dBm
RSL > -85dBm
RSL < -75dBm
Homework 1 - assigned

13. Appendix – Normal distribution table